All categories

1 month ago

The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =

Mathematics

2 answers:

Svet_ta [12.7K]1 month ago

5 0

We start with

$f(x)=x^{2}-2x-3$

To find the roots, set the function to zero

$x^{2}-2x-3=0$

Cluster like terms and shift the constant to the opposite side

$x^{2}-2x=3$

Complete the square, ensuring to maintain equation balance by adding the same constants to both sides.

$x^{2}-2x+1=3+1$

$x^{2}-2x+1=4$

Rewrite in the form of perfect squares

$(x-1)^{2}=4$

Take the square root of both sides

$(x-1)=(+/-)2$

$x=1(+/-)2$

$x=1+2=3$

$x=1-2=-1$

Thus,

the answer is

$x=3$

babunello [11.8K]1 month ago

3 0

X^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

Solving yields x + 1 = 0
Thus, x = -1

Also from x - 3 = 0
We find x = 3

Therefore, the missing value is 3.

You might be interested in

A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was

PIT_PIT [12445]

Answer:

Option C: 0.28

Detailed explanation:

This situation presents a binomial probability distribution.

We need to determine the likelihood that at least 2 thumbtacks land point up out of 5 tossed ones. This can be expressed as;

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)

Referring to the histogram;

P(5) = 0.02

P(4) = 0.02

P(3) = 0.05

P(2) = 0.19

Consequently;

P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02

P(X ≥ 2) = 0.28

8 0

1 month ago

Read 2 more answers

The equation that represents the canned goods order is 24x + 64y = 384, where x = number of minutes for producing fruit cans and

PIT_PIT [12445]

Answer:

The y-intercept represents the number of minutes allocated for creating vegetable cans when no time is dedicated to fruit cans.

Step-by-step explanation:

The problem indicates that y refers to the minutes spent on vegetable can production, and the y-intercept indicates the y-value where x equals zero.

Thus, the y-intercept signifies the duration for producing vegetable cans when no time has been utilized for fruit can production.

6 0

2 months ago

Read 2 more answers

El perímetro de un rectángulo es 28cm, uno de los lados es 6cm más que el otro lado. Hallar el mayor lado del rectángulo.

Inessa [12570]

Answer: El lado mayor del rectángulo mide 10cm

Step-by-step explanation:

El perímetro de un rectángulo está dado por:

P = 2*L + 2*A

Donde L es la longitud y A es el ancho.

Como sabemos que un lado es 6cm más largo que el otro, podemos expresar esto como:

L = A + 6cm.

Por lo tanto, P = 28cm = 2*L + 2*A

Sustituyendo la primera ecuación en la segunda tenemos:

28cm = 2*(A + 6cm) + 2*A

28cm = 12cm + 4*A

28cm - 12cm = 4*A

16cm/4 = A

4cm = A.

Así que el ancho es 4 cm y la longitud se calcula como L = 4cm + 6cm = 10cm

4 0

2 months ago

Rajan had 6000 RS in his bank account on a particular day a week later he deposited 150p RS and next day he had withdraw 1/3rd o

babunello [11817]

Answer: After the withdrawal, Rajan's bank balance will be

6150 RS - 2050 RS = 4100 RS

Step-by-step explanation:

Initially, Rajan had 6000 RS in his bank account about a week ago. This indicates that the initial balance he possessed is 6000 RS.

One week later, he credited 150p RS to his account.

Thus, the current total in his account is

= 6000 RS + 150p RS = 6150 RS.

The following day, he withdrew one-third of his total balance. Therefore, the amount withdrawn is

1/3 × 6150 = 6150/3 = 2050 RS

After the withdrawal, his remaining balance in the bank will be the new total minus the amount withdrawn.

His remaining balance in the bank account post-withdrawal will be

6150 RS - 2050 RS = 4100 RS

4 0

1 month ago

The profit function P(x), revenue function, R(x), and cost function, C(x), are related by the equation P(x) = R(x) – C(x). Andre

Svet_ta [12734]

Answer: 8x - 1200

Step-by-step explanation: I solved the problem

3 0

1 month ago